References
Araki, S.: On root systems and an infinitesimal classification of irreducible symmetric spaces. J. of Math., Osaka City Univ.13, 1–34 (1962)
Bérard, P. H.: On the wave equation on a compact Riemannian manifold without conjugate points. Math. Z.155, 249–276 (1977)
Borel, A.: Compact Clifford-Klein forms of symmetric spaces. Topology2, 111–122 (1963)
Colin de Verdière, Y.: Spectre conjoint d'opérateurs pseudo-différentiels qui commutent, I. Le cas non intégrable. Preprint, Institut Fourier, St. Martin d'Hères. (1978)
DeGeorge, D.L., Wallach, N.R.: Limit formulas for multiplicities inL 2 (Γ/G). Ann. of Math.107, 133–150 (1978)
Duistermaat, J.J., Guillemin, V.W.: The spectrum of positive elliptic operators and periodic bicharacteristics. Invent. Math.29, 39–79 (1975)
Gangolli, R.: Asymptotic behaviour of spectra of compact quotients of certain symmetric spaces. Acta Math.121, 151–192 (1968)
Gangolli, R.: On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups. Ann. of Math.93, 150–165 (1971)
Gangolli, R.: Spectra of discrete uniform subgroups of semisimple Lie groups. In: Symmetric Spaces. Short Courses Presented at Washington University, pp. 93–117. New York: Marcel Dekker 1972
Gangolli, R., Warner, G.: On Selberg's trace formula. J. Math. Soc. Japan27, 327–343 (1975)
Gel'fand, I.M.: Automorphic functions and the theory of representations. Proc. Int. Congr. of Math., Stockholm, 1962, pp. 74–85. Stockholm: Almquist & Wiksell 1963
Gel'fand, I.M., Graev, M.I.: Geometry of homogenoues spaces, representations of groups in homogeneous spaces, and related questions of integral geometry, I. Trudy. Moskov. mat. Obšč.8, 321–390 (1959)
Gindikin, S.G., Karpelevič, F.I.: Plancherel measure of Riemannian symmetric spaces of nonpositive curvature. Dokl. Akad. Nauk SSSR145, 252–255 (1962)
Harish-Chandra: On the Plancherel formula for the right-invariant functions on a semisimple Lie group. Proc. Nat. Acad. Sci. U.S.A.40, 200–204 (1954)
Harish-Chandra: The Plancherel formula for complex semisimple Lie groups. Trans. Amer. Math. Soc.76, 485–528 (1954)
Harish-Chandra: Differential operators on a semisimple Lie algebra. Amer. J. Math.79, 87–120 (1957)
Harish-Chandra: A formula for semisimple Lie groups. Amer. J. Math.79, 733–760 (1957)
Harish-Chandra: Spherical functions on a semisimple Lie group. I Amer. J. Math.80, 241–310 (1958)
Harish-Chandra: Spherical functions on a semisimple Lie group. II. Amer. J. Math.80, 553–613 (1958)
Harish-Chandra: Invariant eigendistributions on a semisimple Lie group. Trans. Amer. Math. Soc.119, 457–508 (1965)
Harish-Chandra: Discrete series for semisimple Lie groups, II. Explicit determination of the characters. Acta Math.116, 1–111 (1966)
Harish-Chandra: Harmonic analysis on real reductive groups, I. The theory of the constant term. J. of Functional Analysis19, 104–204 (1975)
Hejhal, D.A.: The Selberg Trace Formula for PSL(2,ℝ), Volume I. Lecture Notes in Math.548. Berlin-Heidelberg-New York: Springer 1976
Helgason, S.: Differential Geometry and Symmetric Spaces. New York: Academic Press 1962
Helgason, S., Johnson, K.: The bounded spherical functions on symmetric spaces. Advances in Math.3, 586–593 (1969)
Hörmander, L.: The spectral function of an elliptic operator. Acta Math.121, 193–218 (1968)
Kolk, J.: Formule de Poisson et distribution asymptotique du spectre simultane d'opérateurs différentiels. C.R. Acad. Sci. Paris Sér. A-B284, 1045–1048 (1977)
Kolk, J.A.C.: The Selberg Trace Formula and Asymptotic Behaviour of Spectra. Thesis, Rijksuniversiteit Utrecht, (1977)
Lax, P.D., Phillips, R.S.: Scattering Theory for Automorphic Functions. Ann. of Math. Studies No 87, Princeton: Princeton University Press 1976
Mackey, G.W.: The Theory of Unitary Group Representations. Chicago: The University of Chicago Press 1976
Menikoff, A., Sjöstrand, J.: On the eigenvalues of a class of hypoelliptic operators. Math. Annalen,235, 55–85 (1978)
Minakshisundaram, S., Pleijel, A.: Some properties of the eigenfunctions of the Laplace-operator on Riemannian maniforlds. Canadian J. Math.1, 242–256 (1949)
Mostow, G.D.: Intersections of discrete subgroups with Cartan subgroups. J. Indian Math. Soc.34, 203–214 (1970)
Mostow, G.D.: Strong Rigidity of Locally Symmetric Spaces. Ann. of Math. Studies No 78. Princeton: Princeton University Press 1973
Ozols, V.: Critical points of the displacement function of an isometry. J. Differential Geometry3, 411–432 (1969)
Prasad, G., Raghunathan, M.S.: Cartan subgroups and lattices in semi-simple groups. Ann. of Math.96, 296–317 (1972)
Randol, B.: On the analytic continuation of the Minakshisundaram-Pleijel zeta function for compact Riemann surfaces. Trans. Amer. Math. Soc.201, 241–246 (1975)
Randol, B.: The Riemann hypothesis for Selberg's zeta-function and the asymptotic behavior of eigenvalues of the Laplace operator. Trans. Amer. Math. Soc.236, 209–223 (1978)
Schiffmann, G.: Intégrales d'entrelacement et fonctions de Whittaker. Bull. Soc. Math. France99, 3–72 (1971)
Selberg, A.: Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc.20, 47–87 (1956)
Varadarajan, V.S.: Lie Groups, Lie Algebras and Their Representations. Englewood Cliffs: Prentice Hall 1974
Varadarajan, V.S.: Harmonic Analysis on Real Reductive Groups. Lecture Notes in Math.576. Berlin-Heidelberg-New York: Springer 1977
Wallach, N.R.: On the Selberg trace formula in the case of compact quotients. Bull. Amer. Math. Soc.82, 171–195 (1976)
Wallach, N.R.: An asymptotic formula of Gelfand and Gangolli for the spectrum of Γ/G. J. Differential Geometry11, 91–101 (1976)
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Work partially done at the Mathematisch Instituut, Rijksuniversiteit Utrecht
Work partially supported by NSF Grant MCS 76-05962. In addition, this author would like to acknowledge his gratefulness to the authorities of the Mathematisch Instituut, Rijksuniversiteit Utrecht and the Mathematisches Institut, Universität Bonn, for their hospitality during the Fall and Winter of 1975, when a part of this work was carried out
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Duistermaat, J.J., Kolk, J.A.C. & Varadarajan, V.S. Spectra of compact locally symmetric manifolds of negative curvature. Invent Math 52, 27–93 (1979). https://doi.org/10.1007/BF01389856
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DOI: https://doi.org/10.1007/BF01389856